Introduction to IMA fractal proceedings * Uniqueness of invariant measures for place-dependent random iterations of functions * Iterated function systems for lossless data compression * From fractal image compression to fractal-based methods in mathematics * Fractal image compression with fast local search * Wavelets are piecewise fractal interpolation functions * Self-affine vector measures and vector calculus on fractals * Using the Picard contraction mapping to solve inverse problems in ordinary differential equations * Fractal modulation and other applications from a theory of the statistics of dimension * Signal enhancement based on Hoelder regularity analysis * Iterated data mining techniques on embedded vector modeling * A web-based fractal geometry course for non-science students
This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. The event was an integral part of the IMA annual program on Mathemat ics in Multimedia, 2000-2001. We would like to thank Michael F. Barnsley (Department of Mathematics and Statistics, University of Melbourne), Di etmar Saupe (Institut fUr Informatik, UniversiUit Leipzig), and Edward R. Vrscay (Department of Applied Mathematics, University of Waterloo) for their excellent work as organizers of the meeting and for editing the proceedings. We take this opportunity to thank the National Science Foundation for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001. The meeting was an exciting and intense one, focused on fractal image compression, analysis, and synthesis, iterated function systems and fractals in education. The central concerns of the meeting were to establish within these areas where we are now and to develop a vision for the future.
This volume describes the status of fractal imaging research and looks to future directions. It will be useful to researchers in the areas of fractal image compression, analysis, and synthesis, iterated function systems, and fractals in education. In particular it includes a vision for the future of these areas.